MinT - Best Known (157−62, 157, s)-Nets in Base 8

Best Known (157−62, 157, s)-Nets in Base 8

(157−62, 157, 354)-Net over F₈ — Constructive and digital

Digital (95, 157, 354)-net over F₈, using

t-expansion [i] based on digital (93, 157, 354)-net over F₈, using
- 15 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(157−62, 157, 384)-Net in Base 8 — Constructive

(95, 157, 384)-net in base 8, using

3 times m-reduction [i] based on (95, 160, 384)-net in base 8, using
- trace code for nets [i] based on (15, 80, 192)-net in base 64, using
  - 4 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
    - base change [i] based on digital (3, 72, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(157−62, 157, 706)-Net over F₈ — Digital

Digital (95, 157, 706)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−62, 157, 66454)-Net in Base 8 — Upper bound on s

There is no (95, 157, 66455)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6099 722998 158706 470469 330681 612306 780213 374505 601067 192565 622570 837649 449936 713342 245047 008910 282135 515805 958614 179170 360298 158243 138480 959232 > 8¹⁵⁷ [i]